- A60
- B62
- C58
- D122
Step-by-Step Solution
A number that leaves remainder 2 on division by 3, 4 and 5 is 2 more than a common multiple of 3, 4 and 5. LCM, so the number is . (60 itself leaves remainder 0; 58 subtracts instead of adding.)
Answer: B) 62
The three number lines mark the numbers that leave remainder 2 when divided by 3, by 4 and by 5 (jumps of 3, 4 and 5 starting at 2). Apart from 2, no number up to 40 is marked on all three. If the jumps continue, what is the smallest number greater than 2 marked on all three lines?
Class 6Playing with NumbersPlaying with Numbers
Key idea: Factors come in pairs
To find every factor of a number, walk up from 1 and check each whole number — if it divides the number with no remainder, it is a factor. Factors come in **pairs**: if 4 is a factor of 12, so is 12 ÷ 4 = 3. So you only need to check up to the square root of the number to find them all. Factors of 12: — six factors total: 1, 2, 3, 4, 6, 12. Every number has 1 and itself as factors.
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